Recently I've been doing some research into the way that different cultures create names out of words with meanings, and then a suffix or a prefix added on, as well as combinations of words. This research is for some writing I've been doing, and I currently need a Greek name with a fairly specific meaning.

I need a name that says "To speak for the people" or "Voice of the people". The best I can come up with is Demosphenios, derived from Demos, meaning people, and Phenai, meaning to speak. However, given my complete lack of knowledge of ancient Greek, can anyone put me right on the correct way of putting such a name? Equally, could anyone come up with a good Greek name to represent "Voice of the people" which would be more suitable for the purpose?

I think 'Demophon' (or more correctly 'Demophoon', with an omega in the end) would be the right combination derived from dèmos and fèmi.

In Greek mythology, Demophon referred to two different kings: one of Eleusis and the other, Athens.

Demophon was a son of King Celeus and Queen Metanira. While Demeter was searching for her daughter, having taken the form of an old woman called Doso, she received a hospitable welcome from Celeus, the King of Eleusis in Attica. He asked her to nurse Demophon and Triptolemus, his sons by Metanira. As a gift to Celeus, because of his hospitality, Demeter planned to make Demophon immortal by burning his mortal spirit away in the family hearth every night. She was unable to complete the ritual because Metanira walked in on her one night. Instead, Demeter chose to teach Triptolemus the art of agriculture and, from him, the rest of Greece learned the plant and reap crops. He flew across the land on a winged chariot while Demeter and Persephone cared for him, and helped him complete his mission of educating the whole of Greece on the art of agriculture.

The other Demophon was a King of Athens who was in Heraclidae, a play by Euripides, starring Macaria, one of the daughters of Heracles. She and her brothers and sisters hid from Eurystheus in Athens, ruled by King Demophon. As Eurystheus prepared to attack, an oracle told Demophon that he would win if and only if a noble woman was sacrificed to Persephone. Macaria volunteered for the sacrifice and a spring was named the Macarian spring in her honor [source]

Yep, both options by Atticus sound good, Theophoon would be correct as well I think, but I haven't found the name anywhere, Theophrastos on the other hand...

As for Laiokoon, I don't know. The Laio could come from laios, that's not hard to see, but I don't know where the suffix "-koon would come from or what it would mean, so it's hard to tell how laios as people would be related to it. But it's certainly possible.